contamination possibility

Is there a possibility of sample contamination if there are some frozen ice outside of the tube? I think it is. But how to prevent this happens. Why there are ice formed around tubes if they are put at -20C?

Of course, there is possibility of contamination. Open -20 for long time causes the formation of ice on tubes but we cannot avoid that. If we need to search for something specific we need to keep open -20 sometimes. You can avoid by keep the tube on ice and wipe it before open.

is the ice inside the tube? if so then it is caused by sublimation and condensation of liquid from the sample. you'll find this happening to many samples that are stored at -20C for extended periods (especially in a frost-free freezer). not only is this not a contaminant but it must be remixed with the remaining sample if you want to maintain its concentration.

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You could try storing the tube with a thin piece of parafilm wrapped around the top. It will keep the water in your sample from evaporating (for a regular 1.5 mL eppendorf) and will keep the edges of the lid clean.